Circuits that provide substantially stable reference voltages under varying conditions have existed for many years. One such circuit is the bandgap voltage reference circuit which is based on the base to emitter voltage (V.sub.BE) of bipolar junction transistors. The circuit typically utilizes two transistors operating at different current densities. A voltage proportional to the difference between the base to emitter voltages (.DELTA.V.sub.BE) of the two transistors is developed within the circuit. Typically, the .DELTA.V.sub.BE voltage developed by the circuit increases with increasing temperature and the V.sub.BE voltage of the transistor decreases with increasing temperature such that the sum of the two voltages can be arranged to be substantially independent of temperature.
FIG. 1 illustrates a voltage reference circuit 10 known to the prior art described in P. R. Gray and R. G. Meyer, Analysis and Design of Analog Integrated Circuits, John Wiley & Sons, New York, N.Y., 1993, at 344-346. In order for a stable operating point to exist, the differential input voltage defined across input terminals 18 and 22 of the operational amplifier 26 must be zero. Thus, the voltage drop across R1 30 must equal the voltage drop across R2 34. Assuming negligible base currents for transistors Q1 38 and Q2 42, a .DELTA.V.sub.BE must exist across resistor R3 46. As the temperature increases, V.sub.BE of Q2 42 decreases. The two currents I.sub.1 32 and I.sub.2 36 must have a ratio determined by the ratio of R1 30 to R2 34. These two currents are the collector currents of the two diode-connected transistors Q1 38 and Q2 42, assuming base currents are negligible. Thus the difference between their base to emitter voltages is ##EQU1##
where I.sub.S1 and I.sub.S2 are the device dependent saturation currents of Q1 38 and Q2 42, respectively. V.sub.T is given by ##EQU2##
where k is Boltzmann's constant, T is the absolute temperature in Kelvin, and q is the charge of an electron. .DELTA.V.sub.BE appears across resistor R3 46 and is proportional to absolute temperature. The same current that flows in R3 46 also flows in R2 34, so that the voltage across R2 34 must be ##EQU3##
The output voltage V.sub.OUT 14 is the sum of the voltage across R1 30 and the voltage across Q1 38. The voltage across R1 30 is equal to that across R2 34 indicated above. The output voltage is thus ##EQU4##
where V.sub.BE1 is the base to emitter voltage of Q1 38.
The resulting V.sub.OUT can be arranged to have an effective temperature coefficient of zero. To achieve this result, the parameters of transistors Q1 38 and Q2 42, and resistors R1 30, R2 34 and R3 46 must be strictly controlled.
FIG. 2 illustrates another prior art voltage reference circuit 50 as disclosed in U.S. Pat. No. 3,887,863. In this circuit, the input signals 54 and 58 to the operational amplifier 62 are proportional to the voltage drops across load resistors R1 64 and R2 68. If the voltage drops are not equal, the operational amplifier output drives the base of transistors Q1 72 and Q2 76 so as to establish equal currents through R1 64 and R2 68. In this example, .DELTA.V.sub.BE is proportional to the voltage measured across resistor R3 80. As the temperature changes the change in .DELTA.V.sub.BE is compensated by the change in voltage across R3 80 such that the voltage drop across the series combination of Q2 76 and R3 80 is equal to the voltage drop across Q1 72. The resulting output voltage (V.sub.OUT) 84 can be arranged to provide a temperature independent voltage reference. Again, proper functioning of this bandgap voltage reference circuit requires critical matching of R1 64, R2 68, R3 80, R4 88, Q1 72 and Q2 76.
These prior art references are representative of efforts to improve the stability of bandgap voltage reference sources at the expense of circuit complexity and an increase in the stringency of the component matching requirements. The present invention provides a bandgap voltage reference circuit capable of operation with a low supply voltage. The circuit has a low device count and reduced component matching requirements without loss of performance.